Magnetic resonance (MR) diffusion imaging has become an established technique for inferring structural anisotropy of tissues, and more particularly for mapping the white matter connectivity of the human brain [1]. The term “diffusion” refers here to the Brownian motion of (typically) water molecules inside tissues, resulting from their thermal energy.
Several mathematical models of molecular diffusion in tissues have been designed, becoming more and more complex over the last decade while attempting to make less and less assumptions. The simplest, and oldest, model is the Diffusion Tensor (DTI) introduced by Basser [2]. According to this model, which is still widely used despite its limitations and the unrealistic assumptions on which is relies, the diffusive properties of a body can be expressed by the six independent elements of a symmetric, bi-dimensional, three-by-three diffusion tensor. Among the more recent and more sophisticated models, the Q-ball model (QBI) introduced by Tuch [3] and belonging to the class of high angular resolution diffusion imaging (HARDI) models, is worth mentioning.
In any case, magnetic resonance diffusion imaging involves acquiring MR signals by applying to said target body a number of spin echo pulse sequences, together with corresponding pairs of diffusion-encoding gradient pulses along a set of non-collinear orientations. The pairs of gradient pulses make the spin echo signals sensible to the diffusion of molecules; more precisely, each spin echo signal is attenuated by a coefficient depending on the “ease” of diffusion of water molecules along a direction aligned with that of the gradient.
By performing a plurality of spin-echo acquisitions sensitized by gradient pulses with different orientations, it is possible to estimate a set of model-dependent parameters characterizing the diffusive properties of the target body. In general, in order to obtain a meaningful estimation of these parameters, the gradient orientations need to be at least approximately uniformly distributed in space. The number of acquisitions to be performed depends on the model, but also on the signal-to-noise ratio and on the required accuracy of the estimation. For example, DTI requires at least six acquisitions (plus a seventh reference acquisition, without gradient pulses) for determining six parameters; but since the acquired signals are unavoidably corrupted by noise, the parameters estimate can be improved by using a significantly higher number of pulse sequences, and therefore of gradient orientation.
In clinical practice the number of acquisitions, and therefore of gradient orientations, is determined a priori on an empirical basis. Then, acquisitions are performed and finally data processing is performed offline.
This way of operating has a number of disadvantages.
First of all, if the patient moves during examination, or if some of the acquired signals turn out to be highly corrupted by nose, all the data have to be discarded and the examination has to be repeated anew, because the current processing methods cannot operate on partial data sets. In order to solve this problem, document [8] provides a method for determining the “best” spatial distribution of the gradient orientations, should the acquisition be terminated before completion. Such a sequence consists of a series of small meaningful subsets of uniform orientations, all subsets complementing each other with additional orientations.
Another drawback of prior art magnetic resonance diffusion imaging technique is that in some cases, the preset number of acquisitions turns out, in hindsight, to be insufficient to allow a reliable estimation of diffusion parameters. In this case, the examination has to be repeated. This is both annoying for the patient and costly for the hospital or examination center.
In order to avoid this event, the number of acquisition is usually set at a comparatively high value. But this means that, in most cases, more acquisitions will be performed than it would really be necessary. As a consequence, the expensive MR apparatuses are not used efficiently.
The method of document [8] is of no help for solving these problems because, like conventional methods, it requires a preset number of acquisitions, even if it allows exploitation of incomplete data sets and can even deal with unexpected early termination of the examination.
Document US 2007/038072 discloses a method for performing magnetic resonance diffusion imaging characterized by the use of an incremental estimator for determining the value of diffusion parameters of a target body. This allows:                reducing the required data storage capacity;        performing at least part of the required computation in parallel with data acquisition; and        obtaining intermediate data, rendering the method at least partially tolerant to early termination.        